In general, to increase the gain, you must increase the efficiency or the directivity. Arrays typically have driven elements with high efficiency, so you have to increase directivity.

Antenna Directivity can be increased with larger antennas (in general more directive than shorter antennas), or using an array with more elements (i.e., increase the net size of the array without introducing grating lobes), or use a sidelobe-minimizing weighting method.

Reflectarray, if i not mistaken, is the combination of phased array and reflector antenna.

It was feed by a horn antenna and each array element (patches in this image) can have different reflection phase by vary the element's geometry.

Each signal path from horn antenna to reflectarray will have different path length.

Quote:

Antenna Directivity can be increased with larger antennas (in general more directive than shorter antennas), or using an array with more elements (i.e., increase the net size of the array without introducing grating lobes), or use a sidelobe-minimizing weighting method.

Can i know what is grating lobes and sidelobe-minimizing weighting method?